The present invention relates to a method for an accelerated test of semiconductor devices whose memory cell comprises a ferroelectric thin film, wherein an information holding life time without power supply is evaluated by temperature acceleration.
Such an accelerated test is useful for evaluating the lifetime of a semiconductor device under a certain condition in a limited period. In the accelerated test an excessive voltage supply or an excessive operating temperature is applied to the device to be tested. Especially, temperature acceleration (an excessive operating temperature) is effective for testing the information holding lifetime of a nonvolatile memory or the deterioration lifetime of a metal junction when an operating voltage is not applied.
In a conventional accelerated temperature test the relationship between the lifetime t.sub.1 under a use operating condition and the lifetime t.sub.2 under an accelerated test condition is defined below using an acceleration factor K. EQU t.sub.1 =K.times.t.sub.2 ( 1)
The acceleration factor K is given below using an activating energy E.sub.a that limits a lifetime. EQU K=exp(E.sub.a /k.times.(1/T.sub.1 -1/T.sub.2)), where T.sub.2 &gt;T.sub.1 ( 2)
Here, k is the Boltzmann's constant and the activation energy E.sub.a is experimentally determined by the temperature dependence of lifetime. For example, the activation energy is given as a gradient of a regression line that is fit to the plots of experimental result showing the relationship between the logarithm of the lifetime and the inverse of the temperature. This is based on an assumption that a probability for the reaction dominating the lifetime depends on the Boltzmann distribution. If two temperatures T.sub.1 and T.sub.2 are given, the acceleration factor K is determined directly from the above equation (2).
A variation of a physical quantity I that decreases along with elapsed can be expressed as a function of temperature and time. As shown in FIG. 7, the logarithm of the decreasing physical quantity I varies linearly (i.e., proportionally) to time t, and the gradient of the variation depends on the temperature. For example, a necessary time for the physical quantity I to vary from I.sub.0 to I' is t.sub.1 ' under a condition of the temperature T.sub.1, and t.sub.2 ' under a condition of the temperature T.sub.2. The relationship between t.sub.1 ' and t.sub.2 ' is expressed by equation (1) using the acceleration factor K.
Similarly, when the physical quantity I varies from I' to I", the relationship between t.sub.1 " and t.sub.2 " is also expressed by the equation (1) using the same acceleration factor K. Thus, the relationship between t.sub.1, and t.sub.2 corresponding to the temperature T.sub.1 and T.sub.2 can be expressed by the equation (1) using the single acceleration factor K, independently from the decreasing rate of the physical quantity. Therefore, even if the lifetime is not defined clearly corresponding to a certain value of the physical quantity, an accelerated stress condition of the time t.sub.2 and the temperature T.sub.2 which is equivalent to a use condition of the time t.sub.1 and temperature T.sub.1 can be calculated using the acceleration factor K.
However, some physical quantities such as magnetization in permanent magnets or polarization charge in nonvolatile memories decrease linearly to a logarithm of time. In this case, the relationship between times t.sub.1 and t.sub.2 corresponding to the temperatures T.sub.1 and T.sub.2 is no longer expressed by equations (1) and (2) using the acceleration factor K. This is further explained below using FIG. 8.
The vertical axis of the coordinate shown in FIG. 8 is the decreasing physical quantity I and the horizontal axis is the logarithm of time t. In this case, the relationship between I and log t is linear. Slope of each line depends on the corresponding temperature. As shown in FIG. 8, t.sub.1 and t.sub.2 have a relationship defined by the following equation using a proportionality factor m at any physical quantity I. EQU m.times.log t.sub.2 =log t.sub.1 ( 3)
Therefore, the relationship between t.sub.1 ' and t.sub.2 ' is EQU t.sub.1 '=t.sub.2 '.sup.m ( 4)
Thus, t.sub.1 '/t.sub.2 '=t.sub.2 '.sup.m-1 and the relationship between t.sub.1 " and t.sub.2 " is expressed in the equation, t.sub.1 "=t.sub.2 ".sup.m-1. Since t.sub.2 ' is not equal to t.sub.2 ", the acceleration factor depends on a the stress time under a certain acceleration condition. Therefore, in this case, the physical quantity such as the lifetime or other measure for decrease can be determined only for a certain value m by calculating the ratio of log t.sub.1 and log t.sub.2.
An information, i.e., a logic state of a nonvolatile memory, is read by a sense amplifier that amplifies the differential voltage between a reference voltage and a voltage on a bit line after transferring an electric charge from a memory cell to the bit line. In this case it is difficult to determine the exact differential voltage (memory window) between the reference voltage and the voltage of the bit line whose logic state cannot be discriminated. Consequently, the required stress time t.sub.2 for the accelerating temperature T.sub.2 cannot be calculated based on the use operating temperature T.sub.1 and the stress time t.sub.1. As a result, it was difficult to perform an accelerated test based on a confident decay model.